Reduction to Bessel's equation

Hi Guys, just hoping someone might be able to shed a little light on the following problem. I'm working my through Kreyzig's Advanced Engineerig Maths and have come unstuck. the given ODE is x^2y''-5xy'+9(x^6-8)y=0
(y=(x^3)*u) ((x^3)=z). The solutions manual gives the following for y prime.
[1] dy/dx=d/dx (x^3)u = 3(x^2)u+(x^3)du/dz*3x^2 = (3x^5)u'+(3x^2)u
Until know I thought I understood the chain rule, but obviously I don't have a clue. Any ideas on how he went from d/dx (x^3)u to (3x^5)u'+(3x^2)u would be very much appreciated.
Cheers DynamicDan

Hi Guys, just hoping someone might be able to shed a little light on the following problem. I'm working my through Kreyzig's Advanced Engineerig Maths and have come unstuck. the given ODE is x^2y''-5xy'+9(x^6-8)y=0
(y=(x^3)*u) ((x^3)=z). The solutions manual gives the following for y prime.
[1] dy/dx=d/dx (x^3)u = 3(x^2)u+(x^3)du/dz*3x^2 = (3x^5)u'+(3x^2)u
Until know I thought I understood the chain rule, but obviously I don't have a clue. Any ideas on how he went from d/dx (x^3)u to (3x^5)u'+(3x^2)u would be very much appreciated.
Cheers DynamicDan

I'm sorry but I can't follow what you've posted. What does (y=(x^3)*u) ((x^3)=z) mean?